What is the general solution for sin(3x)-sin(5x)=0 ?

The general solution for sin(3x)-sin(5x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=2pin,x=pi+2pin

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sin(3x)-sin(5x)=0

sin (3 x) - sin (5 x) = 0

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = 2 πn, x = π + 2 πn

Solution steps

sin (3 x) - sin (5 x) = 0

Rewrite using trig identities

- 2 cos (4 x) sin (x) = 0

Solving each part separately

cos (4 x) = 0 or sin (x) = 0

cos (4 x) = 0 : x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = 2 πn, x = π + 2 πn

tan (x) = \frac{5}{13}

2 sec (θ) - 7 = 0

tan (x) = 23

- 4 sin (2 x) - 4 cos (x) = 0

2 sin^{2} (4 x) - 2 cos (4 x) = 1, o^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for sin(3x)-sin(5x)=0 ?
The general solution for sin(3x)-sin(5x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=2pin,x=pi+2pin